Question

what is the surface area of the cylinder with height 8 mi and radius 2 mi? round your answer to the nearest thousandth.

Explanation:

Step1: Recall the formula for the surface area of a cylinder

The formula for the surface area of a cylinder is \(S = 2\pi r^{2}+2\pi rh\), where \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 2\) mi and \(h=8\) mi.
First, calculate \(2\pi r^{2}\):
\(2\pi r^{2}=2\pi\times(2)^{2}=2\pi\times4 = 8\pi\)
Then, calculate \(2\pi rh\):
\(2\pi rh=2\pi\times2\times8=32\pi\)

Step3: Add the two parts together

\(S=8\pi + 32\pi=40\pi\)

Step4: Calculate the numerical value

Using \(\pi\approx3.14159265\), we have \(S = 40\times3.14159265=125.663706\)

Answer:

\(125.664\)